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PROBLEMAS 1) El rendimiento del motor de la figura es del 90% y eleva a un
cuerpo de 100 kg mediante el juego de poleas indicado en la figura. Si el cuerpo M se encontraba inicialmente en reposo sobre el suelo, si durante todo el ascenso el cable es recogido por el motor con una aceleración aA = 10 cm/s2 (aceleración del punto A del cable) y en un determinado instante la velocidad del cable en A es vA= 1 m/s, determinar en dicho instante (todas las respuestas tienen que venir razonadas, demostradas o apoyadas en algún tipo de cálculo matemático para ser consideradas válidas): a) la velocidad del bloque M, b) la tensión en la cuerda que tira del bloque M, c) la tensión de la cuerda del motor, d) la potencia suministrada al motor para su funcionamiento. e) Calcular también la potencia media que se le suministra al motor durante todo el ascenso del
bloque M desde el instante inicial en el que partió hasta el instante considerado en los apartados anteriores.
Las masas de las poleas y del cable se consideran despreciables. Tómese g =9.8 m/s2. SOLUCION
a) El hecho de que el punto A está unido a un punto fijo (eje de la polea grande) por una cuerda de
longitud determinada impone una relación entre el movimiento de dicho punto y del cuerpo M. Cuando el punto A se desplaza una cierta distancia hacia la izquierda el cuerpo M asciende una distancia mitad (ver figura). Si los desplazamientos de M son siempre la mitad de los desplazamientos de A, derivando obtenemos que la relación entre velocidades es similar, y volviendo a derivar obtenemos que la relación entre aceleraciones es similar:
b) Aplicando la segunda ley de Newton para el cuerpo M: TM −Mg = MaM ⇒ TM = M g + aM( ) =
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vM = 12vA = 0.5 m/s aM = 1
2aA = 5 cm/s
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